When an inertial unit is switched on, it is known that it is essential to initialize the unit so that the angle, velocity, and position data delivered at the time of initialization correspond exactly to the attitude, velocity, and position applicable to said inertial unit at the instant it is initialized. The data delivered by the said unit after it has been initialized is obtained by integrating gyro and accelerometer measurements starting from the initial data, such that any error in initialization gives rise to increasing errors subsequently.
When the carried vehicle (missile, aircraft, helicopter, torpedo, etc. . . . ) provided with an inertial unit is carried by a carrier vehicle (ship, aircraft, truck, submarine, etc. . . . ) that is likewise fitted with an operating inertial unit, it is common practice to initialize the inertial unit of said carried vehicle prior to said carrier vehicle leaving the carrier vehicle on the basis of data delivered by the inertial unit of the carrier vehicle. Such a procedure of initializing one inertial unit on the other is called "alignment".
It may be observed that during such initialization, there is generally no difficulty in aligning velocity and position since the relative position of the two inertial units is known exactly. In contrast, it is difficult to obtain angle alignment since the relative orientation of the two inertial units is not known exactly.
In what follows, it is only angular alignment of two inertial units that is taken into consideration, and not their alignment in velocity and position. In addition, for the purpose of simplifying explanation, it is assumed that each inertial unit is referenced in conventional manner on an intrinsic system of orthogonal reference axes ("an intrinsic reference axis system") comprising two horizontal axes, one of which (axis N) points north, another of which (axis E) points east, and the third of which is a vertical axis (axis Z), such that for said inertial unit attitudes are defined by three angles respectively called .psi. (i.e. psi=heading, relative to axis N), .theta. (i.e. theta=trim angle relative to the plane of the axes N and E) and .phi. (i.e. phi=roll angle), velocity is defined by three velocity components VN, VE, and VZ (relative to said axes N, E, and Z, respectively), and position is defined by three coordinates .lambda., G, and z which correspond respectively to latitude, to longitude, and to altitude. Naturally such a system of reference axes is given merely to facilitate explanation. The invention is not limited to this system and in the context of the present invention the system could be replaced by some other reference system.
It will be observed that the three angles .psi., .theta., and .phi. transform the intrinsic reference axis system to the physical axis system tied to the inertial unit under consideration.
Conversely, the angle measurements .psi., .theta., and .phi. in an inertial unit serve to define the calculation reference axis system of the unit.
On the basis of axes that are physically tied to the unit, the inverse rotations (-.phi. measured, then -.theta. measured, then -.psi. measured) transform to the calculation reference axis system which coincides with the intrinsic reference axis system if the measurements are perfect.
Thus, a set of rotations (.phi.1, .phi.2, .phi.3) is defined for transforming from the intrinsic reference system to the calculation reference axis system, with .phi.1, .phi.2, and .phi.3 corresponding respectively to rotations about the North axis, about the East axis, and about the vertical axis of the intrinsic reference axis system.
Further, the term "harmonization" angle errors (h1, h2, h3) is used for angle errors concerning knowledge of the orientation of the axes that are physically tied to the inertial unit of the carried vehicle, with h1, h2, and h3 corresponding to rotations about respective ones of said axes.
Ignoring the drift of the gyro systems, it may be observed that .phi.1, .phi.2, and .phi.3 are substantially constant in the North, East, and vertical axis system, and that h1, h2, and h3 which physically represent mechanical setting errors are substantially constant in a system of axes tied physically to the inertial unit of the carried vehicle.
By projecting the harmonization errors h1, h2, and h3 on the axes of the intrinsic reference system, errors h1V, h2V, h3C are defined which are thus not constant when the attitude of the carrier changes, with h1V and h2V corresponding to vertical harmonization errors and with h3C corresponding to a heading harmonization error.
Several methods are already known for angularly aligning one inertial unit on another.
In the following explanation, it may be assumed that the inertial units of the carrier vehicle and of the carried vehicle are parallel once their relative angular position is known, thereby simplifying the explanation.
The simplest method consists, at the time the inertial unit of the carried vehicle is initialized, in copying the angles .psi., .theta., and .phi. into it from the inertial unit of the carrier vehicle. Then, to avoid the influence of noise affecting the angles of the inertial unit of the carrier vehicle at the time of initialization, the copy is followed by servo-controlling the data .psi., .theta., and .phi. of the unit in the carried vehicle for a certain length of time and in a closed loop on the corresponding data of the unit in the carrier vehicle, thereby achieving filtering that eliminates the influence of said noise. However, this method assumes that the two inertial units are parallel (or that the relative orientation thereof is known). In the general case where the relative orientation of the two inertial units is not known accurately, copying angles under servo-control leaves said harmonization errors intact between the respective calculation reference axis systems of the two units, which errors are due to lack of parallelism between or to lack of knowledge about the relative angular positions of the two inertial units.
Another method is derived from that described in the work entitled NAVIGATION INERTIELLE OPTIMALE ET FILTRAGE STATISTIQUE (in translation: Optimum inertial navigation and statistical filtering) by FAURRE, CAMBERLEIN and CHEVREUIL, published by Dunod, 1971, Chapter 11. That work deals with aligning a fixed inertial unit.
However, by considering changes in accelerometer data between two moving inertial units, instead of considering data from the fixed inertial unit, the case of aligning a fixed unit can be generalized to aligning a moving unit on another unit subjected to the same motion. In that method, after similar initialization of .psi., .theta., and .phi., the vertical is aligned by closed loop servo-control on the basis of velocity or acceleration errors relative to the N axes and to the E axes of the two calculation reference systems, and by servo-controlling the heading. In this method, advantage is taken of the fact that for a rectilinear trajectory at constant speed, the measured acceleration errors .DELTA..gamma.N and .DELTA..gamma.E relative to the N and E axes of the calculation reference system in each of the two inertial units are of the following types: EQU .DELTA..gamma.N=-g.phi.2 (1) EQU .DELTA..gamma.E=g.phi.1 (2)
where g is the acceleration due to gravity and .phi.1 and .phi.2 are respective angle offsets defined above. Thus, starting from measurements of .DELTA..gamma.N and .DELTA..gamma.E, it is possible to calculate rotation commands .phi.1co and .phi.2co about the North and East axes respectively of the calculation reference system of the inertial unit in the carried vehicle, and to apply these commands to the inertial unit of the carried vehicle via a second order servo-control loop, i.e. a loop including integration. Thus, after the rotations about the axes N and E, the vertical axes Z of the calculation reference systems of the two units move into alignment after the servo-control has converged, at the end of which time the commands being passed .phi.1co and .phi.2co are respectively equal to .DELTA..gamma.Eo/g and -.DELTA..gamma.No/g where .DELTA..gamma.Eo and .DELTA..gamma.No are the (noise-free) mean acceleration errors prior to switching on the servo-control. It then suffices to servo-control (in the manner described above for the angles .psi., .theta., and .phi.) simultaneously the heading .psi. of the carried vehicle inertial unit on the heading of the carrier vehicle inertial unit to achieve overall alignment. This method suffers from the drawback of requiring the trajectory of the carrier vehicle at the time of initialization to be rectilinear and at constant speed, and it leaves a systematic error constituted by the heading harmonization error.
Kalman filters have already been used to align one inertial unit on another. Such a method is described, for example, in the following works:
KALMAN FILTER FORMULATIONS FOR TRANSFER ALIGNMENT OF STRAPDOWN INERTIAL UNITS, by Alan M. SCHNEIDER, NAVIGATION, Journal of the Institute of Navigation, Vol. 30, No. 1, Spring 1983, pages 72 to 89;
THE ENIGMA OF FALSE BIAS DETECTION IN A STRAPDOWN SYSTEM DURING TRANSFER ALIGNMENT, by I. Y. BAR-ITZHACK and Y. VITEK, Journal of Guidance, Vol. 8, No. 2, March-April 1985, pages 175 to 180;
RAPID TRANSFER ALIGNMENT FOR TACTICAL WEAPON APPLICATIONS by James E. KAIN and James R. CLOUTIER, proceedings of the conference of the American Institute of Aeronautics and Astronautics, 370, 1'Enfant Promenade, S.W. Washington, D.C. 20024, "Guidance Navigation and Control Conference," Boston, Aug. 14-16, 1989.
This method of alignment by Kalman filtering is based on the fact that if .phi.1, .phi.2, and .phi.3 are as defined above, the following may be written: EQU .DELTA..gamma.N=.gamma.E..phi.3-.gamma.Z..phi.2 (3) EQU .DELTA..gamma.E=-.gamma.N..phi.3+.gamma.Z..phi.1 (4)
in which .gamma.N, .gamma.E, and .gamma.Z are respectively the accelerations along the North, East, and vertical axes of the inertial unit of the carrier vehicle, and .DELTA..gamma.N and .DELTA..gamma.E are the acceleration differences measured by the two units along their own calculation reference North and East axes.
It may be observed that if the carrier vehicle moves at constant velocity, .gamma.N=.gamma.E=0 and .gamma.Z=g. Under such circumstances, equations 3 and 4 reduce respectively to above equations 1 and 2.
Thus, in the context of a Kalman filter state X.sup.T =[.DELTA.VN, .DELTA.VE, .phi.1, .phi.2, .phi.3] driven by the velocity measurement [.DELTA.VN, .DELTA.VE] or the acceleration measurements .DELTA..gamma.N, .DELTA..gamma.E, use is made of equations 3 and 4, and the state model is: EQU .DELTA.VN=.gamma.E..phi.3-.gamma.Z..phi.2 EQU .DELTA.VE=-.gamma.N..phi.3+.gamma.Z..phi.1 EQU .phi.1=0 EQU .phi.2=0 EQU .phi.3=0 (I)
The filter may further include, without changing its operating principles:
a measurement of the vertical velocity difference .DELTA.VZ and of the vertical acceleration difference .DELTA..gamma.Z; and
the addition of the following rate of change equation in its model EQU .DELTA.VZ=-.gamma.E..phi.1+.gamma.N..phi.2
A more complex state model could include modelling the errors in the instrumentation of the carried unit (gyro drift, accelerometer bias, etc. . . .). The carried unit is first initialized (.psi., .theta., .phi.) on the basis of the corresponding data of the carrier unit, and then the Kalman filter is put into operation.
It may be observed in the context of this method of alignment by means of Kalman filtering that:
if the carrier vehicle is travelling at constant velocity, then equations (3) and (4) reduce to equations (1) and (2), so the method provides no means of estimating the heading error .phi.3. The theoretical heading error is then the sum of the heading harmonization error h3C and the heading initialization error;
if the carrier vehicle is moving so that the rate of change of .gamma.E and .gamma.Z, and also of .gamma.N and .gamma.Z are not proportional, they can be distinguished from each other and the system is said to be "observable". The Kalman filter can then estimate the three errors .phi.1, .phi.2, and .phi.3, and is thus capable of performing alignment without significant theoretical error; and
if the trajectory of the carrier vehicle gives rise to little contrast between the rates of change of .gamma.E and .gamma.Z, and of .gamma.N and .gamma.Z, then the system has low observeability, and the estimates of .phi.1, .phi.2, and .phi.3 are poor, particularly with respect to the heading error .phi.3 which includes the influence of the heading harmonization error and the influence of the heading initialization error. The method of alignment by Kalman filtering is then not usable.
An object of the present invention is to remedy the drawbacks of the three known methods recalled above, and it provides a system making it possible simultaneously:
to avoid imposing a precise trajectory on the carrier vehicle;
to estimate the errors .phi.1, .phi.2, and .phi.3 providing the trajectory of the carrier vehicle makes the system observable;
if the observeability of the system by the trajectory of the carrier vehicle is low or zero, to leave only the heading harmonization error as a main error; and
depending on circumstances, to identify the harmonization errors between the two inertial units:
for the vertical and for heading if the trajectory of the carrier vehicle makes the system observable; or
for the vertical only if constant velocity and a rectilinear trajectory prevent the heading error being observable.